I've heard of cell phone batteries exploding on occasion when not connected to the wall. In fact, it's not only cell phones.
One way to tell if your battery in your cell phone is starting to act up is to check to see how hot the phone is. If it's warm or cool, talk away. The minute it starts to get too warm, hang up. If it gets hot, replace the battery. You probably don't need to replace the phone.
The problem is probably not the phone being connected to the outlet (the electric power going to the phone is only around 3 volts); the problem is a defective battery. Lithium-ion batteries have a history of volatility. Improvements in lithium-ion battery design may be mitigating this problem, but one must remember that batteries are packages of chemical soup and can be volatile.
Other things using the lithium-ion battery: laptop computers, Chevrolet Volt ("... have its gigantic cell phone battery explode you to bits ..." [NYTimes, 8/11/2009])
Nice having a chemical factory next to your ear, eh?
(Thanks to Gizmodo, the Gadget Blog for the photo!)
